The aggregate “portfolio”: Econometrics of economic rates of return with a Portuguese illustration

Abstract

Abstract. This research forwards estimation procedures – applications of weighted and generalized least squares techniques - designed to infer expected values, variances and covariances of rates of return in the presence of variously correlated sample observations but uncorrelated “sample waves” (strata of) and availability of already aggregate data – under which inference must rely on averages (means) of averages of averages... The same principles are extended to the method of order statistics, appropriate for univariate inference of a truncated distribution parameters. Simple tests of portfolio – market - efficiency based on correlations (or special rank correlations) between actual and estimated optimal shares are also proposed. Illustrative estimates for Portuguese economic sectors are provided – relying on yearly, semi-aggregate information for firms with 20 or more employees, covering the period 1996-2002: on the one hand, sector means, variances and covariances of economic returns to unitary (tangible and intangible asset) applications are presented and reduced by principal components. On the other, optimal (“unrestricted”) portfolios for nested subsets are reported, having been generated by a stepwise elimination procedure. Industries’ betas are approximated and market efficiency tested. Finally, parameter MOS estimates under (univariate) truncated normal assumptions are obtained.

Keywords. Industry economic rates of return; Firm size; Optimal portfolio; Mean – Variance; CAPM; Market efficiency; Weighted least squares; “Weighted” SUR; Weighted method of order statistics; Weighted principal components; Dummy variables. Index numbers; Aggregation.

JEL. G11; G12; G30. C39; C43; C51; C61. C24. L16; L25.